## Lectures & Tutorials

- Spring 2021/2022
- When and where = Fridays (9:00-11:30) in T10 (Troja)
- Language: Czech or English
- Requirements for exam: To pass the exam, students should prove understanding of the fundamental parts of the theory and ability to solve typical problems.
- To get to the exam, students have to solve a project assignment, pass a midterm (písemka v půlce semestru), and solve the homeworks.
- Assignments and study materials will be available in MS Teams.
- Some content is based on our book.

### Lectures

**Approximate syllabus (will be adapted to the students):**

- Principle of least action, Hamilton canonical equations. Cornerstones of differential geometry, Lie groups and algebras, duals of Lie algebras. Euler-Poincare equations, rigid body rotation. Infinite-dimensional Lie groups and fluid mechanics.
- Lagrangian and Eulerian fluid mechanics, solids, viscoelastic fluids.
- Principle of maximum entropy. Liouville and Boltzmann entropy. Sackur-Tetrode relation for ideal gases.
- Reversibility and irreversibility. Dissipation potential. Energetic and entropic representations. Second law of thermodynamics.
- General Equation for Non-equilibrium Reversible-Irreversible Coupling (GENERIC).
- Liouville equation and kinetic theory. Electromagnetic fields and their interaction with matter.
- Mixtures, hyperbolic evolution and Maxwell-Stefan equation, Fick's and Ohm's law. Hyperbolic heat conduction and Fourier's law.
- Fluctuations, Wiener processes, fluctuation dissipation theorem, Fokker-Planck equation, Ito calculus.

### Lectures

- More details on Teams.